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Oksanka [162]
3 years ago
15

Mrs. Sahd distributes pencils and papers to students in the ratio of 2 pencils to 10 sheets of paper. Three of these ratios are

equivalent to 2/10. which one is not? a. 1/5 b. 7/15 c. 4/20 d. 8/40?
Mathematics
1 answer:
IRINA_888 [86]3 years ago
5 0

The ratio that is not equivalent is B. 7:15

The reason why it's not equivalent because for the other ratios:

1:5 could be turned into 2:10 by multiplying 1 and 5 by 2.

4:20 could turn into 2:10 by dividing both numbers by 2.

And 8:40 could be divided by 4 to get 2:10.

But you can't do anything to 7:15 to make it 2:10.

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Answer:

b.  \displaystyle \frac{1}{2}

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Order of Operations: BPEMDAS

  1. Brackets
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  3. Exponents
  4. Multiplication
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  6. Addition
  7. Subtraction
  • Left to Right<u> </u>

<u>Algebra I</u>

  • Functions
  • Function Notation
  • Exponential Rule [Rewrite]:                                                                              \displaystyle b^{-m} = \frac{1}{b^m}
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<u>Calculus</u>

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Derivative Notation

Basic Power Rule:

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Derivative Rule [Chain Rule]:                                                                                       \displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)

Step-by-step explanation:

<u>Step 1: Define</u>

<em>Identify</em>

<em />\displaystyle H(x) = \sqrt[3]{F(x)}<em />

<em />

<u>Step 2: Differentiate</u>

  1. Rewrite function [Exponential Rule - Root Rewrite]:                                      \displaystyle H(x) = [F(x)]^\bigg{\frac{1}{3}}
  2. Chain Rule:                                                                                                        \displaystyle H'(x) = \frac{d}{dx} \bigg[ [F(x)]^\bigg{\frac{1}{3}} \bigg] \cdot \frac{d}{dx}[F(x)]
  3. Basic Power Rule:                                                                                             \displaystyle H'(x) = \frac{1}{3}[F(x)]^\bigg{\frac{1}{3} - 1} \cdot F'(x)
  4. Simplify:                                                                                                             \displaystyle H'(x) = \frac{F'(x)}{3}[F(x)]^\bigg{\frac{-2}{3}}
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  2. Substitute in function values:                                                                          \displaystyle H'(5) = \frac{6}{3(8)^\bigg{\frac{2}{3}}}
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Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Derivatives

Book: College Calculus 10e

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